EULERIANITY OF FOURIER COEFFICIENTS OF AUTOMORPHIC FORMS
Artikel i vetenskaplig tidskrift, 2021

We study the question of Eulerianity (factorizability) for Fourier coefficients of automorphic forms, and we prove a general transfer theorem that allows one to deduce the Eulerianity of certain coefficients from that of another coefficient. We also establish a ‘hidden' invariance property of Fourier coefficients. We apply these results to minimal and next-to-minimal automorphic representations, and deduce Eulerianity for a large class of Fourier and Fourier-Jacobi coefficients. In particular, we prove Eulerianity for parabolic Fourier coefficients with characters of maximal rank for a class of Eisenstein series in minimal and next-to-minimal representations of groups of ADE-type that are of interest in string theory.

Euler product

nilpotent orbit

Eisenstein series

minimal representation

next-to-minimal representation

Whittaker support

automorphic forms

wave-front set

automorphic representation

Fourier coefficients on reductive groups

Fourier-Jacobi coefficients

Författare

Dmitry Gourevitch

Weizmann Institute of Science

Henrik Gustafsson

Institute for Advanced Studies

Rutgers University

Chalmers, Matematiska vetenskaper, Algebra och geometri

Axel Kleinschmidt

Max-Planck-Gesellschaft

Université libre de Bruxelles (ULB)

Daniel Persson

Chalmers, Matematiska vetenskaper, Algebra och geometri

Siddhartha Sahi

Rutgers University

Representation Theory

1088-4165 (ISSN)

Vol. 25 481-507

Små automorfa representationer

Vetenskapsrådet (VR) (2018-04760), 2019-01-01 -- 2022-12-31.

Ämneskategorier

Geometri

Diskret matematik

Matematisk analys

DOI

10.1090/ert/565

Mer information

Senast uppdaterat

2021-07-05